Crate abax 

abax

A high-performance Rust library for statistical computing and special mathematical functions. abax provides numerically stable and high-precision implementations of probability distributions, error functions, and gamma-related functions.

Features

Probability Distributions

Comprehensive support for Probability Density Functions (PDF), Cumulative Distribution Functions (CDF), and Quantile Functions (Inverse CDF) for common distributions:

• Continuous: Normal, Lognormal, Student’s T, Noncentral T, F, Gamma, Beta, Exponential, Chi-squared, Weibull, Extreme Value, Generalized Extreme Value.
• Discrete: Binomial, Poisson.

Special Functions

• Gamma Family: Gamma, Log-Gamma, Digamma, Trigamma, Tetragamma, and Polygamma (${\psi }^{\left(n\right)}$).
• Incomplete Gamma: Regularized incomplete gamma functions and their inverses.
• Beta Family: Beta, Log-Beta, and Regularized Incomplete Beta functions.
• Error Functions: Erf, Erfc, Erfcx, and their high-precision inverses.
• Bessel Functions: Modified Bessel function of the first kind ($I_{\nu }\left(x\right)$).

Constants

Provides high-precision mathematical constants including:

• Bernoulli numbers ($B_{2n}$)
• Riemann Zeta values ($\zeta \left(s\right)$)
• Stirling series coefficients

Functions

besseli

Compute the modified Bessel function of the first kind $I_\nu(x)$ for non-negative real input.

beta

Beta function $B(z,w)=\frac{\Gamma \left(z\right)\Gamma \left(w\right)}{\Gamma (z+w)}$.

betacdf

Beta cumulative distribution function (CDF).

betainc

Regularized incomplete beta function $I_x(z,w)$.

betaincinv

Inverse of the regularized incomplete beta function.

betainv

Inverse of the beta cumulative distribution function (CDF).

betaln

Natural logarithm of the Beta function.

betapdf

Beta probability density function (PDF).

binocdf

Binomial cumulative distribution function (CDF).

binoinv

Inverse of the binomial cumulative distribution function (CDF).

binopdf

Binomial probability density function (PDF).

chi2cdf

Chi-squared cumulative distribution function (CDF).

chi2inv

Inverse of the Chi-squared cumulative distribution function (quantile function).

chi2pdf

Chi-squared probability density function (PDF).

digamma

Computes the digamma function, $\psi \left(x\right)$, the logarithmic derivative of the Gamma function: $\psi \left(x\right)=\frac{d}{dx}\ln \Gamma \left(x\right)$.

erf

Calculates the error function $\mathrm{erf}\left(x\right)$.

erfc

Calculates the complementary error function erfc(x).

erfcinv

Calculates the inverse complementary error function erfc⁻¹(x).

erfinv

Calculates the inverse error function erf⁻¹(x).

evcdf

Extreme value cumulative distribution function (CDF) for scalar values.

evinv

Extreme value inverse cumulative distribution function (quantile function) for scalar values.

evpdf

Extreme value probability density function (PDF) for scalar values.

expcdf

Exponential cumulative distribution function (CDF).

expinv

Inverse of the exponential cumulative distribution function (quantile function).

exppdf

Calculates the probability density function (PDF) of the exponential distribution at a given value x with scale parameter mu.

fcdf

F cumulative distribution function (CDF).

finv

F inverse cumulative distribution function (quantile function).

fpdf

F probability density function (PDF).

gamcdf

Gamma cumulative distribution function (CDF).

gaminv

Inverse Gamma cumulative distribution function (CDF).

gamma

Calculates the Gamma function Γ(x) using the Lanczos approximation.

gammainc

Computes the regularized incomplete gamma function with optional scaling.

gammaincinv

Inverse of the regularized incomplete gamma function.

gammaln

Computes the natural logarithm of the Gamma function, $\ln \left(\Gamma \right(x\left)\right)$.

gampdf

Gamma probability density function (PDF).

gevcdf

Generalized Extreme Value (GEV) cumulative distribution function (CDF) for scalar values.

gevinv

Generalized Extreme Value (GEV) inverse cumulative distribution function (quantile function) for scalar values.

gevpdf

Calculates the Generalized Extreme Value (GEV) probability density function (PDF) for a single scalar value.

logncdf

Lognormal cumulative distribution function (CDF).

logninv

Inverse of the lognormal cumulative distribution function (CDF).

lognpdf

Lognormal probability density function (PDF).

nctcdf

Noncentral T cumulative distribution function (CDF).

nctinv

Inverse of the noncentral T cumulative distribution function (CDF).

nctpdf

Noncentral T probability density function (PDF).

normcdf

Normal cumulative distribution function (CDF).

norminv

Inverse of the normal cumulative distribution function (quantile function).

normpdf

Normal probability density function (PDF).

poisscdf

Poisson cumulative distribution function (CDF).

poissinv

Inverse of the Poisson cumulative distribution function for scalar values.

poisspdf

Poisson probability density function (PDF).

psi

Computes the polygamma function psi(k, x), where k = 0 is the digamma function and k >= 1 are higher derivatives.

tcdf

Student’s T cumulative distribution function (CDF).

tetragamma

Computes the tetragamma function, ${\psi }^{\left(}\left(x\right)$, the second derivative of the digamma function.

tinv

Inverse of Student’s T cumulative distribution function (CDF).

tpdf

Student’s T probability density function (PDF).

trigamma

Computes the trigamma function, ${\psi }^{\left(}\left(x\right)$, the first derivative of the digamma function: ${\psi }^{\left(}\left(x\right)=\frac{d^2}{d{x}^2}\ln \Gamma \left(x\right)$.

wblcdf

Weibull cumulative distribution function (CDF) for scalar values.

wblinv

Weibull inverse cumulative distribution function (quantile function) for scalar values.

wblpdf

Weibull probability density function (PDF) for scalar values.